Regression Models MA data analysis

Additive Multiple Linear Model

all, solid, and liquid food waste

## Response food_waste_kg :
## 
## Call:
## lm(formula = food_waste_kg ~ var., data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9444 -0.6870 -0.1213  0.5307  3.2825 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -1.4487861  0.7001179  -2.069   0.0403 *  
## var.temp_c     0.0028126  0.0086899   0.324   0.7466    
## var.humi_p     0.0053388  0.0073629   0.725   0.4695    
## var.prcp_mm   -0.0417248  0.0396404  -1.053   0.2942    
## var.tueE       0.1706132  0.1857893   0.918   0.3599    
## var.wedE      -0.1088752  0.1849244  -0.589   0.5569    
## var.thuE      -0.3865671  0.1787284  -2.163   0.0322 *  
## var.friE       0.1925727  0.1752651   1.099   0.2737    
## var.satE      -0.2594445  0.1845003  -1.406   0.1618    
## var.container  0.2795788  0.1621429   1.724   0.0867 .  
## var.liquors    0.0060825  0.0523540   0.116   0.9077    
## var.sales      0.0039416  0.0005678   6.942 1.13e-10 ***
## var.halfs      0.0691157  0.0283383   2.439   0.0159 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9858 on 148 degrees of freedom
## Multiple R-squared:  0.543,  Adjusted R-squared:  0.506 
## F-statistic: 14.66 on 12 and 148 DF,  p-value: < 2.2e-16
## 
## 
## Response solid_waste_kg :
## 
## Call:
## lm(formula = solid_waste_kg ~ var., data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.77317 -0.26285 -0.08542  0.17375  2.23890 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -0.3393464  0.2891174  -1.174   0.2424    
## var.temp_c    -0.0018981  0.0035885  -0.529   0.5976    
## var.humi_p     0.0010506  0.0030406   0.346   0.7302    
## var.prcp_mm   -0.0173666  0.0163697  -1.061   0.2905    
## var.tueE       0.1472586  0.0767227   1.919   0.0569 .  
## var.wedE      -0.0170184  0.0763655  -0.223   0.8240    
## var.thuE      -0.1422127  0.0738068  -1.927   0.0559 .  
## var.friE       0.0577250  0.0723767   0.798   0.4264    
## var.satE      -0.0972288  0.0761904  -1.276   0.2039    
## var.container -0.0292830  0.0669578  -0.437   0.6625    
## var.liquors    0.0078168  0.0216199   0.362   0.7182    
## var.sales      0.0012807  0.0002345   5.462 1.94e-07 ***
## var.halfs      0.0138583  0.0117024   1.184   0.2382    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4071 on 148 degrees of freedom
## Multiple R-squared:  0.3845, Adjusted R-squared:  0.3346 
## F-statistic: 7.704 on 12 and 148 DF,  p-value: 5.36e-11
## 
## 
## Response liquid_waste_kg :
## 
## Call:
## lm(formula = liquid_waste_kg ~ var., data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.42750 -0.48344 -0.07879  0.44523  1.80789 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -1.1094396  0.4911865  -2.259  0.02536 *  
## var.temp_c     0.0047107  0.0060966   0.773  0.44095    
## var.humi_p     0.0042882  0.0051656   0.830  0.40780    
## var.prcp_mm   -0.0243582  0.0278108  -0.876  0.38253    
## var.tueE       0.0233546  0.1303455   0.179  0.85805    
## var.wedE      -0.0918567  0.1297387  -0.708  0.48005    
## var.thuE      -0.2443544  0.1253917  -1.949  0.05322 .  
## var.friE       0.1348477  0.1229620   1.097  0.27457    
## var.satE      -0.1622157  0.1294412  -1.253  0.21211    
## var.container  0.3088618  0.1137557   2.715  0.00741 ** 
## var.liquors   -0.0017344  0.0367304  -0.047  0.96240    
## var.sales      0.0026609  0.0003983   6.680 4.52e-10 ***
## var.halfs      0.0552573  0.0198815   2.779  0.00615 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6916 on 148 degrees of freedom
## Multiple R-squared:  0.5535, Adjusted R-squared:  0.5173 
## F-statistic: 15.29 on 12 and 148 DF,  p-value: < 2.2e-16

Coefficients Visualization

Additive Multiple Linear Model per Customer

all, solid, and liquid per Customer

## Response food_waste_p_kg :
## 
## Call:
## lm(formula = food_waste_p_kg ~ var., data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.070808 -0.025440 -0.002235  0.020112  0.146466 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    3.970e-02  2.660e-02   1.492    0.138  
## var.temp_c     1.395e-04  3.301e-04   0.423    0.673  
## var.humi_p     5.093e-05  2.797e-04   0.182    0.856  
## var.prcp_mm   -1.914e-03  1.506e-03  -1.271    0.206  
## var.tueE       5.465e-03  7.058e-03   0.774    0.440  
## var.wedE      -6.143e-03  7.025e-03  -0.874    0.383  
## var.thuE      -7.898e-03  6.790e-03  -1.163    0.247  
## var.friE       8.833e-03  6.658e-03   1.327    0.187  
## var.satE      -1.050e-02  7.009e-03  -1.499    0.136  
## var.container  1.533e-02  6.160e-03   2.488    0.014 *
## var.liquors    1.945e-03  1.989e-03   0.978    0.330  
## var.sales      3.475e-05  2.157e-05   1.611    0.109  
## var.halfs      6.672e-04  1.077e-03   0.620    0.536  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03745 on 148 degrees of freedom
## Multiple R-squared:  0.1602, Adjusted R-squared:  0.09214 
## F-statistic: 2.353 on 12 and 148 DF,  p-value: 0.008537
## 
## 
## Response solid_waste_p_kg :
## 
## Call:
## lm(formula = solid_waste_p_kg ~ var., data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.027111 -0.009757 -0.001349  0.007366  0.101048 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    2.035e-02  1.107e-02   1.838   0.0680 .
## var.temp_c    -4.721e-05  1.374e-04  -0.344   0.7316  
## var.humi_p    -3.825e-05  1.164e-04  -0.329   0.7430  
## var.prcp_mm   -8.164e-04  6.267e-04  -1.303   0.1947  
## var.tueE       5.960e-03  2.937e-03   2.029   0.0442 *
## var.wedE      -2.923e-04  2.924e-03  -0.100   0.9205  
## var.thuE      -3.814e-03  2.826e-03  -1.350   0.1792  
## var.friE       1.786e-03  2.771e-03   0.645   0.5202  
## var.satE      -3.992e-03  2.917e-03  -1.368   0.1732  
## var.container -9.782e-05  2.563e-03  -0.038   0.9696  
## var.liquors    6.219e-04  8.277e-04   0.751   0.4537  
## var.sales      1.336e-05  8.976e-06   1.489   0.1387  
## var.halfs     -2.354e-04  4.480e-04  -0.525   0.6001  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01559 on 148 degrees of freedom
## Multiple R-squared:  0.09039,    Adjusted R-squared:  0.01664 
## F-statistic: 1.226 on 12 and 148 DF,  p-value: 0.2707
## 
## 
## Response liquid_waste_p_kg :
## 
## Call:
## lm(formula = liquid_waste_p_kg ~ var., data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.04658 -0.01829 -0.00111  0.01530  0.07904 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    1.935e-02  1.875e-02   1.032 0.303893    
## var.temp_c     1.867e-04  2.328e-04   0.802 0.423722    
## var.humi_p     8.918e-05  1.972e-04   0.452 0.651806    
## var.prcp_mm   -1.098e-03  1.062e-03  -1.034 0.302856    
## var.tueE      -4.951e-04  4.977e-03  -0.099 0.920881    
## var.wedE      -5.851e-03  4.953e-03  -1.181 0.239422    
## var.thuE      -4.084e-03  4.787e-03  -0.853 0.394946    
## var.friE       7.047e-03  4.695e-03   1.501 0.135461    
## var.satE      -6.512e-03  4.942e-03  -1.318 0.189633    
## var.container  1.542e-02  4.343e-03   3.551 0.000515 ***
## var.liquors    1.323e-03  1.402e-03   0.943 0.347015    
## var.sales      2.139e-05  1.521e-05   1.406 0.161732    
## var.halfs      9.026e-04  7.591e-04   1.189 0.236315    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02641 on 148 degrees of freedom
## Multiple R-squared:  0.209,  Adjusted R-squared:  0.1449 
## F-statistic:  3.26 on 12 and 148 DF,  p-value: 0.0003427

Per Customer Coefficients Visualization

Scatter plot

Food waste plots

## per Customer

Per Customer RDiT Model

Interaction

## 
## Call:
## lm(formula = rdt_int_fw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.085830 -0.026913 -0.000256  0.022668  0.144070 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.0634025  0.0084860   7.471 5.19e-12 ***
## container       0.0205965  0.0123107   1.673   0.0963 .  
## time           -0.0002550  0.0001694  -1.505   0.1344    
## container:time  0.0002948  0.0002683   1.099   0.2736    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03901 on 157 degrees of freedom
## Multiple R-squared:  0.03369,    Adjusted R-squared:  0.01523 
## F-statistic: 1.825 on 3 and 157 DF,  p-value: 0.1449
## 
## Call:
## lm(formula = rdt_int_sfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.025637 -0.009649 -0.001998  0.007429  0.107324 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     2.413e-02  3.438e-03   7.018 6.35e-11 ***
## container       6.087e-04  4.988e-03   0.122    0.903    
## time           -6.278e-05  6.865e-05  -0.914    0.362    
## container:time  7.849e-05  1.087e-04   0.722    0.471    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0158 on 157 degrees of freedom
## Multiple R-squared:  0.00791,    Adjusted R-squared:  -0.01105 
## F-statistic: 0.4173 on 3 and 157 DF,  p-value: 0.7408
## 
## Call:
## lm(formula = rdt_int_lfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.060368 -0.021770  0.000354  0.019225  0.067531 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.0392726  0.0060700   6.470 1.19e-09 ***
## container       0.0199878  0.0088058   2.270   0.0246 *  
## time           -0.0001922  0.0001212  -1.586   0.1148    
## container:time  0.0002163  0.0001919   1.127   0.2615    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0279 on 157 degrees of freedom
## Multiple R-squared:  0.06328,    Adjusted R-squared:  0.04538 
## F-statistic: 3.535 on 3 and 157 DF,  p-value: 0.01621

Ass-Interaction

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## OK: Error variance appears to be homoscedastic (p = 0.560).
## OK: Error variance appears to be homoscedastic (p = 0.085).
## OK: Error variance appears to be homoscedastic (p = 0.357).
## OK: residuals appear as normally distributed (p = 0.310).
## Warning: Non-normality of residuals detected (p < .001).
## OK: residuals appear as normally distributed (p = 0.506).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_fw_p
## BP = 0.39927, df = 3, p-value = 0.9404
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_sfw_p
## BP = 0.78557, df = 3, p-value = 0.8529
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_lfw_p
## BP = 1.5608, df = 3, p-value = 0.6683
## OK: Residuals appear to be independent and not autocorrelated (p = 0.658).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.810).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.596).

Multiple model

## 
## Call:
## lm(formula = rdt_multi_fw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.072101 -0.025127 -0.002875  0.021863  0.143927 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     2.660e-02  3.639e-02   0.731   0.4659  
## container       2.407e-02  1.377e-02   1.748   0.0826 .
## time           -1.939e-04  2.477e-04  -0.783   0.4351  
## temp_c         -1.276e-04  4.770e-04  -0.267   0.7895  
## humi_p          1.038e-04  3.522e-04   0.295   0.7686  
## prcp_mm        -1.816e-03  1.523e-03  -1.192   0.2350  
## tueE            5.051e-03  7.111e-03   0.710   0.4786  
## wedE           -6.214e-03  7.058e-03  -0.880   0.3801  
## thuE           -7.499e-03  6.849e-03  -1.095   0.2753  
## friE            9.197e-03  6.710e-03   1.371   0.1726  
## satE           -1.057e-02  7.043e-03  -1.500   0.1357  
## liquors         2.100e-03  2.007e-03   1.046   0.2972  
## sales           3.340e-05  2.176e-05   1.535   0.1269  
## halfs           7.956e-04  1.102e-03   0.722   0.4713  
## container:time  1.712e-04  3.772e-04   0.454   0.6505  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03762 on 146 degrees of freedom
## Multiple R-squared:  0.164,  Adjusted R-squared:  0.08388 
## F-statistic: 2.046 on 14 and 146 DF,  p-value: 0.01809
## 
## Call:
## lm(formula = rdt_multi_sfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.027746 -0.009421 -0.001271  0.007188  0.099959 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     1.814e-02  1.514e-02   1.198   0.2328  
## container       4.031e-03  5.730e-03   0.704   0.4829  
## time           -6.248e-05  1.031e-04  -0.606   0.5454  
## temp_c         -1.325e-04  1.985e-04  -0.667   0.5056  
## humi_p         -4.745e-05  1.466e-04  -0.324   0.7466  
## prcp_mm        -7.615e-04  6.338e-04  -1.201   0.2315  
## tueE            5.830e-03  2.959e-03   1.970   0.0507 .
## wedE           -3.105e-04  2.937e-03  -0.106   0.9160  
## thuE           -3.720e-03  2.850e-03  -1.305   0.1939  
## friE            1.964e-03  2.792e-03   0.703   0.4831  
## satE           -3.993e-03  2.931e-03  -1.362   0.1752  
## liquors         6.823e-04  8.353e-04   0.817   0.4154  
## sales           1.301e-05  9.054e-06   1.437   0.1528  
## halfs          -2.071e-04  4.584e-04  -0.452   0.6520  
## container:time  1.911e-05  1.570e-04   0.122   0.9032  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01566 on 146 degrees of freedom
## Multiple R-squared:  0.09445,    Adjusted R-squared:  0.007612 
## F-statistic: 1.088 on 14 and 146 DF,  p-value: 0.3734
## 
## Call:
## lm(formula = rdt_multi_lfw_p, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.04632 -0.01854 -0.00070  0.01527  0.08045 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     8.457e-03  2.566e-02   0.330   0.7422  
## container       2.004e-02  9.712e-03   2.063   0.0409 *
## time           -1.314e-04  1.747e-04  -0.752   0.4532  
## temp_c          4.903e-06  3.364e-04   0.015   0.9884  
## humi_p          1.512e-04  2.484e-04   0.609   0.5436  
## prcp_mm        -1.054e-03  1.074e-03  -0.982   0.3279  
## tueE           -7.794e-04  5.015e-03  -0.155   0.8767  
## wedE           -5.904e-03  4.978e-03  -1.186   0.2376  
## thuE           -3.779e-03  4.831e-03  -0.782   0.4353  
## friE            7.233e-03  4.732e-03   1.528   0.1286  
## satE           -6.574e-03  4.968e-03  -1.323   0.1878  
## liquors         1.418e-03  1.416e-03   1.001   0.3182  
## sales           2.039e-05  1.534e-05   1.329   0.1860  
## halfs           1.003e-03  7.769e-04   1.291   0.1989  
## container:time  1.521e-04  2.660e-04   0.572   0.5683  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02653 on 146 degrees of freedom
## Multiple R-squared:  0.2121, Adjusted R-squared:  0.1365 
## F-statistic: 2.807 on 14 and 146 DF,  p-value: 0.0009764

Ass-Multiple

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## OK: Error variance appears to be homoscedastic (p = 0.162).
## Warning: Heteroscedasticity (non-constant error variance) detected (p < .001).
## OK: Error variance appears to be homoscedastic (p = 0.502).
## Warning: Non-normality of residuals detected (p = 0.007).
## Warning: Non-normality of residuals detected (p < .001).
## OK: residuals appear as normally distributed (p = 0.051).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_fw_p
## BP = 19.644, df = 14, p-value = 0.1418
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_sfw_p
## BP = 13.384, df = 14, p-value = 0.4965
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_lfw_p
## BP = 22.99, df = 14, p-value = 0.06044
## OK: Residuals appear to be independent and not autocorrelated (p = 0.916).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.918).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.966).

Quadratic model

## 
## Call:
## lm(formula = rdt_poly_fw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.075784 -0.024038 -0.004693  0.022090  0.143015 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)
## (Intercept)          2.126e-02  3.914e-02   0.543    0.588
## container            1.627e-02  1.956e-02   0.832    0.407
## time                -3.785e-04  7.018e-04  -0.539    0.591
## I(time^2)           -2.444e-06  7.590e-06  -0.322    0.748
## tueE                 5.662e-03  7.157e-03   0.791    0.430
## wedE                -5.892e-03  7.087e-03  -0.831    0.407
## thuE                -7.233e-03  6.881e-03  -1.051    0.295
## friE                 9.309e-03  6.737e-03   1.382    0.169
## satE                -1.116e-02  7.088e-03  -1.574    0.118
## temp_c              -6.843e-05  4.818e-04  -0.142    0.887
## humi_p               1.319e-04  3.566e-04   0.370    0.712
## prcp_mm             -2.151e-03  1.561e-03  -1.378    0.170
## liquors              2.183e-03  2.016e-03   1.083    0.281
## sales                3.543e-05  2.195e-05   1.614    0.109
## halfs                7.890e-04  1.111e-03   0.710    0.479
## container:time       1.176e-03  1.107e-03   1.062    0.290
## container:I(time^2) -8.586e-06  1.299e-05  -0.661    0.510
## 
## Residual standard error: 0.03773 on 144 degrees of freedom
## Multiple R-squared:  0.1705, Adjusted R-squared:  0.07835 
## F-statistic:  1.85 on 16 and 144 DF,  p-value: 0.02995
## 
## Call:
## lm(formula = rdt_poly_sfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.028366 -0.009439 -0.001808  0.007616  0.097711 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)  
## (Intercept)          9.961e-03  1.622e-02   0.614   0.5400  
## container            5.805e-03  8.106e-03   0.716   0.4751  
## time                -4.231e-04  2.908e-04  -1.455   0.1478  
## I(time^2)           -4.268e-06  3.145e-06  -1.357   0.1769  
## tueE                 6.034e-03  2.965e-03   2.035   0.0437 *
## wedE                -2.115e-04  2.936e-03  -0.072   0.9427  
## thuE                -3.469e-03  2.851e-03  -1.217   0.2258  
## friE                 2.139e-03  2.791e-03   0.766   0.4447  
## satE                -4.316e-03  2.937e-03  -1.470   0.1439  
## temp_c              -1.111e-04  1.996e-04  -0.557   0.5786  
## humi_p              -1.691e-05  1.478e-04  -0.114   0.9091  
## prcp_mm             -9.357e-04  6.468e-04  -1.447   0.1502  
## liquors              7.561e-04  8.355e-04   0.905   0.3670  
## sales                1.452e-05  9.095e-06   1.596   0.1126  
## halfs               -2.637e-04  4.605e-04  -0.573   0.5678  
## container:time       6.496e-04  4.587e-04   1.416   0.1589  
## container:I(time^2)  7.259e-07  5.382e-06   0.135   0.8929  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01564 on 144 degrees of freedom
## Multiple R-squared:  0.1093, Adjusted R-squared:  0.0103 
## F-statistic: 1.104 on 16 and 144 DF,  p-value: 0.3566
## 
## Call:
## lm(formula = rdt_poly_lfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.047637 -0.017604 -0.002375  0.018056  0.078992 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)
## (Intercept)          1.130e-02  2.761e-02   0.409    0.683
## container            1.047e-02  1.380e-02   0.759    0.449
## time                 4.463e-05  4.950e-04   0.090    0.928
## I(time^2)            1.824e-06  5.354e-06   0.341    0.734
## tueE                -3.722e-04  5.048e-03  -0.074    0.941
## wedE                -5.680e-03  4.999e-03  -1.136    0.258
## thuE                -3.764e-03  4.854e-03  -0.776    0.439
## friE                 7.170e-03  4.752e-03   1.509    0.134
## satE                -6.840e-03  4.999e-03  -1.368    0.173
## temp_c               4.269e-05  3.398e-04   0.126    0.900
## humi_p               1.488e-04  2.516e-04   0.592    0.555
## prcp_mm             -1.215e-03  1.101e-03  -1.104    0.272
## liquors              1.427e-03  1.422e-03   1.003    0.317
## sales                2.091e-05  1.548e-05   1.351    0.179
## halfs                1.053e-03  7.840e-04   1.343    0.181
## container:time       5.266e-04  7.809e-04   0.674    0.501
## container:I(time^2) -9.311e-06  9.162e-06  -1.016    0.311
## 
## Residual standard error: 0.02662 on 144 degrees of freedom
## Multiple R-squared:  0.2181, Adjusted R-squared:  0.1312 
## F-statistic:  2.51 on 16 and 144 DF,  p-value: 0.002032

Ass-Poly

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## OK: Error variance appears to be homoscedastic (p = 0.205).
## Warning: Heteroscedasticity (non-constant error variance) detected (p < .001).
## OK: Error variance appears to be homoscedastic (p = 0.347).
## Warning: Non-normality of residuals detected (p = 0.010).
## Warning: Non-normality of residuals detected (p < .001).
## Warning: Non-normality of residuals detected (p = 0.031).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_fw_p
## BP = 22.633, df = 16, p-value = 0.1239
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_sfw_p
## BP = 14.63, df = 16, p-value = 0.5519
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_lfw_p
## BP = 25.091, df = 16, p-value = 0.06823
## OK: Residuals appear to be independent and not autocorrelated (p = 0.856).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.994).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.970).

Cubic model

## 
## Call:
## lm(formula = rdt_poly3_fw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.075520 -0.024226 -0.004963  0.022584  0.143894 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)  
## (Intercept)          9.024e-03  3.975e-02   0.227   0.8207  
## container            3.122e-02  2.404e-02   1.298   0.1962  
## time                -3.086e-03  1.753e-03  -1.761   0.0805 .
## I(time^2)           -8.230e-05  4.819e-05  -1.708   0.0898 .
## I(time^3)           -6.122e-07  3.647e-07  -1.679   0.0954 .
## temp_c               1.379e-04  5.181e-04   0.266   0.7905  
## humi_p               7.087e-05  3.587e-04   0.198   0.8436  
## prcp_mm             -2.587e-03  1.579e-03  -1.638   0.1036  
## tueE                 6.553e-03  7.154e-03   0.916   0.3612  
## wedE                -5.454e-03  7.071e-03  -0.771   0.4418  
## thuE                -6.963e-03  6.862e-03  -1.015   0.3120  
## friE                 8.961e-03  6.720e-03   1.333   0.1845  
## satE                -1.098e-02  7.072e-03  -1.552   0.1228  
## liquors              1.762e-03  2.026e-03   0.870   0.3859  
## sales                3.614e-05  2.191e-05   1.649   0.1013  
## halfs                1.003e-03  1.116e-03   0.899   0.3703  
## container:time       4.270e-03  2.679e-03   1.594   0.1132  
## container:I(time^2)  5.948e-05  8.195e-05   0.726   0.4692  
## container:I(time^3)  7.061e-07  6.606e-07   1.069   0.2869  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03762 on 142 degrees of freedom
## Multiple R-squared:  0.187,  Adjusted R-squared:  0.084 
## F-statistic: 1.815 on 18 and 142 DF,  p-value: 0.02867
## 
## Call:
## lm(formula = rdt_poly3_sfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.028278 -0.009977 -0.001132  0.007785  0.098181 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)  
## (Intercept)          4.344e-03  1.643e-02   0.264   0.7918  
## container            1.316e-02  9.936e-03   1.324   0.1876  
## time                -1.692e-03  7.243e-04  -2.337   0.0209 *
## I(time^2)           -4.175e-05  1.991e-05  -2.097   0.0378 *
## I(time^3)           -2.873e-07  1.507e-07  -1.907   0.0586 .
## temp_c              -9.640e-06  2.141e-04  -0.045   0.9642  
## humi_p              -4.643e-05  1.482e-04  -0.313   0.7546  
## prcp_mm             -1.136e-03  6.525e-04  -1.741   0.0838 .
## tueE                 6.450e-03  2.956e-03   2.182   0.0308 *
## wedE                -2.273e-06  2.922e-03  -0.001   0.9994  
## thuE                -3.343e-03  2.836e-03  -1.179   0.2404  
## friE                 1.981e-03  2.777e-03   0.713   0.4768  
## satE                -4.243e-03  2.922e-03  -1.452   0.1488  
## liquors              5.621e-04  8.373e-04   0.671   0.5031  
## sales                1.488e-05  9.054e-06   1.644   0.1024  
## halfs               -1.655e-04  4.613e-04  -0.359   0.7202  
## container:time       2.035e-03  1.107e-03   1.838   0.0682 .
## container:I(time^2)  3.491e-05  3.386e-05   1.031   0.3043  
## container:I(time^3)  3.111e-07  2.730e-07   1.140   0.2563  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01554 on 142 degrees of freedom
## Multiple R-squared:  0.1318, Adjusted R-squared:  0.02172 
## F-statistic: 1.197 on 18 and 142 DF,  p-value: 0.2709
## 
## Call:
## lm(formula = rdt_poly3_lfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.047242 -0.017433 -0.003693  0.018696  0.077431 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)
## (Intercept)          4.680e-03  2.816e-02   0.166    0.868
## container            1.806e-02  1.703e-02   1.061    0.291
## time                -1.394e-03  1.242e-03  -1.122    0.264
## I(time^2)           -4.055e-05  3.414e-05  -1.188    0.237
## I(time^3)           -3.249e-07  2.583e-07  -1.258    0.211
## temp_c               1.476e-04  3.671e-04   0.402    0.688
## humi_p               1.173e-04  2.541e-04   0.462    0.645
## prcp_mm             -1.451e-03  1.119e-03  -1.297    0.197
## tueE                 1.030e-04  5.068e-03   0.020    0.984
## wedE                -5.451e-03  5.009e-03  -1.088    0.278
## thuE                -3.620e-03  4.861e-03  -0.745    0.458
## friE                 6.980e-03  4.761e-03   1.466    0.145
## satE                -6.735e-03  5.010e-03  -1.344    0.181
## liquors              1.200e-03  1.435e-03   0.836    0.404
## sales                2.125e-05  1.552e-05   1.369    0.173
## halfs                1.169e-03  7.908e-04   1.478    0.142
## container:time       2.235e-03  1.898e-03   1.178    0.241
## container:I(time^2)  2.457e-05  5.806e-05   0.423    0.673
## container:I(time^3)  3.950e-07  4.680e-07   0.844    0.400
## 
## Residual standard error: 0.02665 on 142 degrees of freedom
## Multiple R-squared:  0.227,  Adjusted R-squared:  0.1291 
## F-statistic: 2.317 on 18 and 142 DF,  p-value: 0.003261

Quartic model

## 
## Call:
## lm(formula = rdt_poly4_fw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.075564 -0.024352 -0.005774  0.020979  0.141212 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)  
## (Intercept)          1.818e-02  4.389e-02   0.414   0.6793  
## container            2.367e-02  3.002e-02   0.788   0.4318  
## time                -1.536e-03  3.531e-03  -0.435   0.6641  
## I(time^2)           -2.986e-06  1.639e-04  -0.018   0.9855  
## I(time^3)            8.122e-07  2.837e-06   0.286   0.7751  
## I(time^4)            8.238e-09  1.628e-08   0.506   0.6135  
## temp_c               1.561e-04  5.236e-04   0.298   0.7661  
## humi_p               4.008e-05  3.659e-04   0.110   0.9129  
## prcp_mm             -2.633e-03  1.595e-03  -1.651   0.1010  
## tueE                 6.883e-03  7.228e-03   0.952   0.3426  
## wedE                -5.223e-03  7.130e-03  -0.733   0.4651  
## thuE                -6.904e-03  6.905e-03  -1.000   0.3192  
## friE                 8.834e-03  6.767e-03   1.305   0.1939  
## satE                -1.128e-02  7.142e-03  -1.580   0.1165  
## liquors              1.782e-03  2.044e-03   0.872   0.3847  
## sales                3.722e-05  2.216e-05   1.680   0.0952 .
## halfs                9.921e-04  1.124e-03   0.883   0.3788  
## container:time       2.885e-03  5.282e-03   0.546   0.5858  
## container:I(time^2) -3.064e-05  2.712e-04  -0.113   0.9102  
## container:I(time^3) -4.873e-07  5.232e-06  -0.093   0.9259  
## container:I(time^4) -9.839e-09  3.345e-08  -0.294   0.7691  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03785 on 140 degrees of freedom
## Multiple R-squared:  0.1886, Adjusted R-squared:  0.07263 
## F-statistic: 1.627 on 20 and 140 DF,  p-value: 0.0542
## 
## Call:
## lm(formula = rdt_poly4_sfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.027203 -0.009031 -0.001323  0.006171  0.094325 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)  
## (Intercept)          1.714e-02  1.791e-02   0.957   0.3401  
## container           -7.359e-04  1.225e-02  -0.060   0.9522  
## time                 4.660e-04  1.441e-03   0.323   0.7469  
## I(time^2)            6.862e-05  6.690e-05   1.026   0.3068  
## I(time^3)            1.692e-06  1.158e-06   1.461   0.1461  
## I(time^4)            1.144e-08  6.642e-09   1.722   0.0872 .
## temp_c               7.181e-06  2.136e-04   0.034   0.9732  
## humi_p              -9.238e-05  1.493e-04  -0.619   0.5371  
## prcp_mm             -1.171e-03  6.510e-04  -1.799   0.0742 .
## tueE                 6.950e-03  2.949e-03   2.356   0.0198 *
## wedE                 3.689e-04  2.910e-03   0.127   0.8993  
## thuE                -3.245e-03  2.818e-03  -1.151   0.2515  
## friE                 1.831e-03  2.762e-03   0.663   0.5085  
## satE                -4.731e-03  2.915e-03  -1.623   0.1068  
## liquors              5.508e-04  8.339e-04   0.660   0.5100  
## sales                1.665e-05  9.043e-06   1.842   0.0677 .
## halfs               -1.877e-04  4.585e-04  -0.409   0.6830  
## container:time       1.100e-03  2.155e-03   0.511   0.6105  
## container:I(time^2) -1.520e-04  1.107e-04  -1.374   0.1718  
## container:I(time^3) -4.991e-08  2.135e-06  -0.023   0.9814  
## container:I(time^4) -2.241e-08  1.365e-08  -1.642   0.1028  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01545 on 140 degrees of freedom
## Multiple R-squared:  0.1549, Adjusted R-squared:  0.03412 
## F-statistic: 1.283 on 20 and 140 DF,  p-value: 0.2003
## 
## Call:
## lm(formula = rdt_poly4_lfw_p, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.048361 -0.018359 -0.002681  0.017483  0.078281 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)
## (Intercept)          1.041e-03  3.109e-02   0.033    0.973
## container            2.440e-02  2.127e-02   1.148    0.253
## time                -2.002e-03  2.501e-03  -0.801    0.425
## I(time^2)           -7.161e-05  1.161e-04  -0.617    0.538
## I(time^3)           -8.799e-07  2.010e-06  -0.438    0.662
## I(time^4)           -3.200e-09  1.153e-08  -0.278    0.782
## temp_c               1.489e-04  3.709e-04   0.401    0.689
## humi_p               1.325e-04  2.592e-04   0.511    0.610
## prcp_mm             -1.462e-03  1.130e-03  -1.294    0.198
## tueE                -6.668e-05  5.120e-03  -0.013    0.990
## wedE                -5.592e-03  5.051e-03  -1.107    0.270
## thuE                -3.659e-03  4.891e-03  -0.748    0.456
## friE                 7.003e-03  4.794e-03   1.461    0.146
## satE                -6.552e-03  5.059e-03  -1.295    0.197
## liquors              1.231e-03  1.448e-03   0.851    0.396
## sales                2.057e-05  1.570e-05   1.311    0.192
## halfs                1.180e-03  7.959e-04   1.482    0.140
## container:time       1.785e-03  3.741e-03   0.477    0.634
## container:I(time^2)  1.214e-04  1.921e-04   0.632    0.529
## container:I(time^3) -4.374e-07  3.706e-06  -0.118    0.906
## container:I(time^4)  1.258e-08  2.370e-08   0.531    0.596
## 
## Residual standard error: 0.02681 on 140 degrees of freedom
## Multiple R-squared:  0.2286, Adjusted R-squared:  0.1184 
## F-statistic: 2.074 on 20 and 140 DF,  p-value: 0.007489

Some model

## 
## Call:
## lm(formula = rdt_sales, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -464.65 -156.75   -7.94  132.75  452.58 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    653.2167    45.3342  14.409   <2e-16 ***
## container      -21.1864    65.7665  -0.322   0.7478    
## time            -2.1632     0.9051  -2.390   0.0180 *  
## container:time   3.0966     1.4334   2.160   0.0323 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 208.4 on 157 degrees of freedom
## Multiple R-squared:  0.07338,    Adjusted R-squared:  0.05568 
## F-statistic: 4.145 on 3 and 157 DF,  p-value: 0.00737
## 
## Call:
## lm(formula = rdt_sales_mult, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -400.38 -104.13   -9.09   93.36  439.38 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     382.140    147.670   2.588   0.0106 *  
## container       -31.487     58.605  -0.537   0.5919    
## time             -1.011      1.049  -0.964   0.3367    
## temp_c            2.704      2.011   1.345   0.1807    
## humi_p            1.429      1.481   0.965   0.3362    
## prcp_mm          -5.455      6.451  -0.846   0.3991    
## liquors          43.158      7.347   5.874 2.59e-08 ***
## halfs            28.934      4.069   7.110 4.23e-11 ***
## container:time    1.546      1.601   0.966   0.3357    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 160.9 on 152 degrees of freedom
## Multiple R-squared:  0.4648, Adjusted R-squared:  0.4366 
## F-statistic:  16.5 on 8 and 152 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = rdt_sales, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -398.79 -101.98   -7.22   94.60  437.60 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         441.27206  157.99058   2.793   0.0059 ** 
## container           -63.00940   83.19361  -0.757   0.4500    
## time                  1.96129    2.97708   0.659   0.5110    
## I(time^2)             0.03465    0.03220   1.076   0.2837    
## temp_c                2.57848    2.03385   1.268   0.2068    
## humi_p                1.20252    1.49982   0.802   0.4239    
## prcp_mm              -4.47457    6.61600  -0.676   0.4999    
## liquors              42.38676    7.40288   5.726 5.44e-08 ***
## halfs                29.22421    4.09386   7.139 3.77e-11 ***
## container:time       -2.27212    4.68807  -0.485   0.6286    
## container:I(time^2)  -0.02417    0.05535  -0.437   0.6630    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 161.4 on 150 degrees of freedom
## Multiple R-squared:  0.4691, Adjusted R-squared:  0.4337 
## F-statistic: 13.25 on 10 and 150 DF,  p-value: < 2.2e-16

Log-Linear RDiT Model

Interaction

## 
## Call:
## lm(formula = rdt_int_fw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.07089 -0.29053  0.07099  0.31294  0.92461 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.899186   0.100117   8.981  7.9e-16 ***
## container       0.125174   0.145241   0.862   0.3901    
## time           -0.003624   0.001999  -1.813   0.0717 .  
## container:time  0.004636   0.003166   1.464   0.1451    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4602 on 157 degrees of freedom
## Multiple R-squared:  0.02157,    Adjusted R-squared:  0.002876 
## F-statistic: 1.154 on 3 and 157 DF,  p-value: 0.3293
## 
## Call:
## lm(formula = rdt_int_sfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.49626 -0.17125 -0.02458  0.17911  0.84798 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.456958   0.058104   7.864 5.59e-13 ***
## container      -0.002367   0.084292  -0.028    0.978    
## time           -0.001638   0.001160  -1.412    0.160    
## container:time  0.001864   0.001837   1.015    0.312    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2671 on 157 degrees of freedom
## Multiple R-squared:  0.0273, Adjusted R-squared:  0.008717 
## F-statistic: 1.469 on 3 and 157 DF,  p-value: 0.2251
## 
## Call:
## lm(formula = rdt_int_lfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.86306 -0.32547  0.08476  0.29523  0.83820 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.647578   0.089499   7.236 1.93e-11 ***
## container       0.172827   0.129837   1.331   0.1851    
## time           -0.003520   0.001787  -1.970   0.0506 .  
## container:time  0.004447   0.002830   1.572   0.1181    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4114 on 157 degrees of freedom
## Multiple R-squared:  0.02936,    Adjusted R-squared:  0.01082 
## F-statistic: 1.583 on 3 and 157 DF,  p-value: 0.1956

Ass-Interaction

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## OK: Error variance appears to be homoscedastic (p = 0.654).
## OK: Error variance appears to be homoscedastic (p = 0.064).
## OK: Error variance appears to be homoscedastic (p = 0.778).
## Warning: Non-normality of residuals detected (p = 0.014).
## Warning: Non-normality of residuals detected (p = 0.044).
## Warning: Non-normality of residuals detected (p = 0.004).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_fw_log
## BP = 1.4669, df = 3, p-value = 0.6899
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_sfw_log
## BP = 3.892, df = 3, p-value = 0.2734
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_int_lfw_log
## BP = 2.2738, df = 3, p-value = 0.5176
## OK: No outliers detected.
## - Based on the following method and threshold: cook (0.8).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (0.8).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (0.8).
## - For variable: (Whole model)
## OK: Residuals appear to be independent and not autocorrelated (p = 0.672).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.688).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.602).

Multiple model

## 
## Call:
## lm(formula = rdt_multi_fw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.70381 -0.21143 -0.01368  0.21472  0.89566 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -0.2025206  0.3094972  -0.654  0.51391    
## container       0.1371993  0.1171206   1.171  0.24333    
## time           -0.0009055  0.0021069  -0.430  0.66799    
## temp_c         -0.0003912  0.0040574  -0.096  0.92332    
## humi_p          0.0021214  0.0029957   0.708  0.47999    
## prcp_mm        -0.0197288  0.0129534  -1.523  0.12991    
## tueE            0.0791179  0.0604806   1.308  0.19288    
## wedE           -0.0539749  0.0600338  -0.899  0.37009    
## thuE           -0.0914458  0.0582575  -1.570  0.11865    
## friE            0.0253774  0.0570715   0.445  0.65722    
## satE           -0.0820893  0.0599080  -1.370  0.17271    
## liquors         0.0099865  0.0170719   0.585  0.55947    
## sales           0.0012110  0.0001851   6.544  9.5e-10 ***
## halfs           0.0311432  0.0093690   3.324  0.00112 ** 
## container:time  0.0011543  0.0032081   0.360  0.71952    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.32 on 146 degrees of freedom
## Multiple R-squared:   0.56,  Adjusted R-squared:  0.5179 
## F-statistic: 13.27 on 14 and 146 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = rdt_multi_sfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41365 -0.15187 -0.03471  0.12691  0.87801 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -0.0830067  0.2039018  -0.407   0.6845    
## container       0.0312116  0.0771610   0.405   0.6864    
## time           -0.0002954  0.0013880  -0.213   0.8318    
## temp_c         -0.0011196  0.0026731  -0.419   0.6759    
## humi_p          0.0002079  0.0019736   0.105   0.9163    
## prcp_mm        -0.0109674  0.0085339  -1.285   0.2008    
## tueE            0.0817078  0.0398456   2.051   0.0421 *  
## wedE           -0.0098532  0.0395513  -0.249   0.8036    
## thuE           -0.0723120  0.0383810  -1.884   0.0615 .  
## friE            0.0170265  0.0375997   0.453   0.6513    
## satE           -0.0516432  0.0394684  -1.308   0.1928    
## liquors         0.0066501  0.0112472   0.591   0.5553    
## sales           0.0007099  0.0001219   5.823 3.54e-08 ***
## halfs           0.0096277  0.0061724   1.560   0.1210    
## container:time -0.0003659  0.0021136  -0.173   0.8628    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2108 on 146 degrees of freedom
## Multiple R-squared:  0.4364, Adjusted R-squared:  0.3823 
## F-statistic: 8.074 on 14 and 146 DF,  p-value: 1.421e-12
## 
## Call:
## lm(formula = rdt_multi_lfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.64161 -0.19503  0.00511  0.19954  0.72644 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -0.3398374  0.2771014  -1.226 0.222022    
## container       0.1723560  0.1048614   1.644 0.102399    
## time           -0.0012647  0.0018863  -0.670 0.503613    
## temp_c         -0.0002052  0.0036327  -0.056 0.955037    
## humi_p          0.0023787  0.0026821   0.887 0.376597    
## prcp_mm        -0.0154073  0.0115976  -1.328 0.186087    
## tueE            0.0226180  0.0541500   0.418 0.676785    
## wedE           -0.0570734  0.0537500  -1.062 0.290065    
## thuE           -0.0728029  0.0521596  -1.396 0.164902    
## friE            0.0353672  0.0510977   0.692 0.489944    
## satE           -0.0588896  0.0536373  -1.098 0.274045    
## liquors         0.0066489  0.0152849   0.435 0.664208    
## sales           0.0010125  0.0001657   6.111 8.56e-09 ***
## halfs           0.0305461  0.0083883   3.642 0.000376 ***
## container:time  0.0018389  0.0028723   0.640 0.523038    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2865 on 146 degrees of freedom
## Multiple R-squared:  0.5622, Adjusted R-squared:  0.5202 
## F-statistic: 13.39 on 14 and 146 DF,  p-value: < 2.2e-16

Ass-Multiple

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.019).
## OK: Error variance appears to be homoscedastic (p = 0.448).
## OK: Error variance appears to be homoscedastic (p = 0.205).
## OK: residuals appear as normally distributed (p = 0.831).
## Warning: Non-normality of residuals detected (p < .001).
## OK: residuals appear as normally distributed (p = 0.695).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_fw_log
## BP = 20.433, df = 14, p-value = 0.1171
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_sfw_log
## BP = 12.468, df = 14, p-value = 0.5688
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_multi_lfw_log
## BP = 12.443, df = 14, p-value = 0.5708
## OK: Residuals appear to be independent and not autocorrelated (p = 0.676).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.564).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.596).

Quadratic model

## 
## Call:
## lm(formula = rdt_poly_fw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.69414 -0.21485 -0.01643  0.20846  0.86740 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -3.143e-01  3.323e-01  -0.946  0.34584    
## container            1.217e-01  1.661e-01   0.732  0.46514    
## time                -5.608e-03  5.959e-03  -0.941  0.34821    
## I(time^2)           -5.680e-05  6.445e-05  -0.881  0.37959    
## tueE                 8.403e-02  6.077e-02   1.383  0.16885    
## wedE                -5.148e-02  6.017e-02  -0.855  0.39370    
## thuE                -8.756e-02  5.843e-02  -1.498  0.13619    
## friE                 2.777e-02  5.720e-02   0.485  0.62812    
## satE                -8.818e-02  6.018e-02  -1.465  0.14505    
## temp_c               1.016e-04  4.091e-03   0.025  0.98023    
## humi_p               2.575e-03  3.028e-03   0.850  0.39655    
## prcp_mm             -2.309e-02  1.325e-02  -1.742  0.08362 .  
## liquors              1.115e-02  1.712e-02   0.651  0.51593    
## sales                1.236e-03  1.864e-04   6.633  6.2e-10 ***
## halfs                3.051e-02  9.438e-03   3.232  0.00152 ** 
## container:time       1.241e-02  9.400e-03   1.320  0.18895    
## container:I(time^2) -3.033e-05  1.103e-04  -0.275  0.78368    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3204 on 144 degrees of freedom
## Multiple R-squared:  0.5649, Adjusted R-squared:  0.5166 
## F-statistic: 11.69 on 16 and 144 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = rdt_poly_sfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37382 -0.14580 -0.02945  0.12595  0.83578 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -2.350e-01  2.169e-01  -1.084   0.2803    
## container            7.135e-02  1.084e-01   0.658   0.5115    
## time                -7.037e-03  3.889e-03  -1.810   0.0724 .  
## I(time^2)           -7.958e-05  4.206e-05  -1.892   0.0605 .  
## tueE                 8.512e-02  3.966e-02   2.146   0.0335 *  
## wedE                -8.221e-03  3.927e-02  -0.209   0.8345    
## thuE                -6.772e-02  3.813e-02  -1.776   0.0778 .  
## friE                 2.029e-02  3.733e-02   0.544   0.5875    
## satE                -5.734e-02  3.927e-02  -1.460   0.1465    
## temp_c              -7.590e-04  2.670e-03  -0.284   0.7766    
## humi_p               7.689e-04  1.976e-03   0.389   0.6978    
## prcp_mm             -1.403e-02  8.650e-03  -1.622   0.1071    
## liquors              7.994e-03  1.117e-02   0.715   0.4755    
## sales                7.370e-04  1.216e-04   6.060 1.13e-08 ***
## halfs                8.552e-03  6.159e-03   1.389   0.1671    
## container:time       1.087e-02  6.134e-03   1.773   0.0784 .  
## container:I(time^2)  2.076e-05  7.197e-05   0.288   0.7734    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2091 on 144 degrees of freedom
## Multiple R-squared:  0.4532, Adjusted R-squared:  0.3924 
## F-statistic: 7.458 on 16 and 144 DF,  p-value: 1.713e-12
## 
## Call:
## lm(formula = rdt_poly_lfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63819 -0.19662  0.00115  0.19553  0.73005 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -3.425e-01  2.983e-01  -1.148 0.252852    
## container            9.485e-02  1.491e-01   0.636 0.525707    
## time                -9.383e-04  5.349e-03  -0.175 0.860998    
## I(time^2)            1.604e-06  5.785e-05   0.028 0.977924    
## tueE                 2.685e-02  5.455e-02   0.492 0.623250    
## wedE                -5.479e-02  5.401e-02  -1.014 0.312064    
## thuE                -7.183e-02  5.245e-02  -1.370 0.172951    
## friE                 3.540e-02  5.135e-02   0.689 0.491645    
## satE                -6.229e-02  5.402e-02  -1.153 0.250828    
## temp_c               1.960e-04  3.672e-03   0.053 0.957513    
## humi_p               2.460e-03  2.718e-03   0.905 0.367005    
## prcp_mm             -1.739e-02  1.190e-02  -1.462 0.145983    
## liquors              6.977e-03  1.537e-02   0.454 0.650533    
## sales                1.022e-03  1.673e-04   6.110 8.85e-09 ***
## halfs                3.079e-02  8.471e-03   3.635 0.000386 ***
## container:time       7.218e-03  8.438e-03   0.855 0.393773    
## container:I(time^2) -7.877e-05  9.900e-05  -0.796 0.427521    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2876 on 144 degrees of freedom
## Multiple R-squared:  0.5649, Adjusted R-squared:  0.5165 
## F-statistic: 11.68 on 16 and 144 DF,  p-value: < 2.2e-16

Ass-Poly

  1. Linearity of the relationships between the dependent and independent variables
  2. Normality of the residuals
  3. Homoscedasticity of the residuals
  4. No influential points (outliers)
  5. No multicollinearity
  6. Independence of the observations
## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.013).
## OK: Error variance appears to be homoscedastic (p = 0.434).
## OK: Error variance appears to be homoscedastic (p = 0.117).
## OK: residuals appear as normally distributed (p = 0.890).
## Warning: Non-normality of residuals detected (p < .001).
## OK: residuals appear as normally distributed (p = 0.613).
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_fw_log
## BP = 24.13, df = 16, p-value = 0.08671
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_sfw_log
## BP = 13.961, df = 16, p-value = 0.6016
## 
##  studentized Breusch-Pagan test
## 
## data:  rdt_poly_lfw_log
## BP = 17.492, df = 16, p-value = 0.3545
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## OK: No outliers detected.
## - Based on the following method and threshold: cook (1).
## - For variable: (Whole model)
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## # Check for Multicollinearity
## 
## Low Correlation
## 
##     Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##     tueE 1.87 [ 1.56,   2.33]         1.37      0.54     [0.43, 0.64]
##     wedE 1.83 [ 1.54,   2.28]         1.35      0.55     [0.44, 0.65]
##     thuE 1.66 [ 1.41,   2.07]         1.29      0.60     [0.48, 0.71]
##     friE 1.65 [ 1.41,   2.06]         1.29      0.60     [0.49, 0.71]
##     satE 1.80 [ 1.51,   2.24]         1.34      0.56     [0.45, 0.66]
##   temp_c 2.34 [ 1.93,   2.95]         1.53      0.43     [0.34, 0.52]
##   humi_p 2.01 [ 1.67,   2.52]         1.42      0.50     [0.40, 0.60]
##  prcp_mm 1.25 [ 1.11,   1.57]         1.12      0.80     [0.64, 0.90]
##  liquors 1.54 [ 1.32,   1.91]         1.24      0.65     [0.52, 0.76]
##    sales 2.49 [ 2.04,   3.14]         1.58      0.40     [0.32, 0.49]
##    halfs 1.48 [ 1.27,   1.83]         1.22      0.68     [0.55, 0.79]
## 
## High Correlation
## 
##                 Term    VIF      VIF 95% CI Increased SE Tolerance
##            container  10.77 [ 8.34,  14.00]         3.28      0.09
##                 time 120.29 [91.79, 157.74]        10.97  8.31e-03
##            I(time^2)  26.34 [20.20,  34.43]         5.13      0.04
##       container:time  77.46 [59.16, 101.53]         8.80      0.01
##  container:I(time^2)  40.40 [30.92,  52.89]         6.36      0.02
##  Tolerance 95% CI
##      [0.07, 0.12]
##      [0.01, 0.01]
##      [0.03, 0.05]
##      [0.01, 0.02]
##      [0.02, 0.03]
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## # Check for Multicollinearity
## 
## Low Correlation
## 
##     Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##     tueE 1.87 [ 1.56,   2.33]         1.37      0.54     [0.43, 0.64]
##     wedE 1.83 [ 1.54,   2.28]         1.35      0.55     [0.44, 0.65]
##     thuE 1.66 [ 1.41,   2.07]         1.29      0.60     [0.48, 0.71]
##     friE 1.65 [ 1.41,   2.06]         1.29      0.60     [0.49, 0.71]
##     satE 1.80 [ 1.51,   2.24]         1.34      0.56     [0.45, 0.66]
##   temp_c 2.34 [ 1.93,   2.95]         1.53      0.43     [0.34, 0.52]
##   humi_p 2.01 [ 1.67,   2.52]         1.42      0.50     [0.40, 0.60]
##  prcp_mm 1.25 [ 1.11,   1.57]         1.12      0.80     [0.64, 0.90]
##  liquors 1.54 [ 1.32,   1.91]         1.24      0.65     [0.52, 0.76]
##    sales 2.49 [ 2.04,   3.14]         1.58      0.40     [0.32, 0.49]
##    halfs 1.48 [ 1.27,   1.83]         1.22      0.68     [0.55, 0.79]
## 
## High Correlation
## 
##                 Term    VIF      VIF 95% CI Increased SE Tolerance
##            container  10.77 [ 8.34,  14.00]         3.28      0.09
##                 time 120.29 [91.79, 157.74]        10.97  8.31e-03
##            I(time^2)  26.34 [20.20,  34.43]         5.13      0.04
##       container:time  77.46 [59.16, 101.53]         8.80      0.01
##  container:I(time^2)  40.40 [30.92,  52.89]         6.36      0.02
##  Tolerance 95% CI
##      [0.07, 0.12]
##      [0.01, 0.01]
##      [0.03, 0.05]
##      [0.01, 0.02]
##      [0.02, 0.03]
## Model has interaction terms. VIFs might be inflated.
##   You may check multicollinearity among predictors of a model without
##   interaction terms.
## # Check for Multicollinearity
## 
## Low Correlation
## 
##     Term  VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##     tueE 1.87 [ 1.56,   2.33]         1.37      0.54     [0.43, 0.64]
##     wedE 1.83 [ 1.54,   2.28]         1.35      0.55     [0.44, 0.65]
##     thuE 1.66 [ 1.41,   2.07]         1.29      0.60     [0.48, 0.71]
##     friE 1.65 [ 1.41,   2.06]         1.29      0.60     [0.49, 0.71]
##     satE 1.80 [ 1.51,   2.24]         1.34      0.56     [0.45, 0.66]
##   temp_c 2.34 [ 1.93,   2.95]         1.53      0.43     [0.34, 0.52]
##   humi_p 2.01 [ 1.67,   2.52]         1.42      0.50     [0.40, 0.60]
##  prcp_mm 1.25 [ 1.11,   1.57]         1.12      0.80     [0.64, 0.90]
##  liquors 1.54 [ 1.32,   1.91]         1.24      0.65     [0.52, 0.76]
##    sales 2.49 [ 2.04,   3.14]         1.58      0.40     [0.32, 0.49]
##    halfs 1.48 [ 1.27,   1.83]         1.22      0.68     [0.55, 0.79]
## 
## High Correlation
## 
##                 Term    VIF      VIF 95% CI Increased SE Tolerance
##            container  10.77 [ 8.34,  14.00]         3.28      0.09
##                 time 120.29 [91.79, 157.74]        10.97  8.31e-03
##            I(time^2)  26.34 [20.20,  34.43]         5.13      0.04
##       container:time  77.46 [59.16, 101.53]         8.80      0.01
##  container:I(time^2)  40.40 [30.92,  52.89]         6.36      0.02
##  Tolerance 95% CI
##      [0.07, 0.12]
##      [0.01, 0.01]
##      [0.03, 0.05]
##      [0.01, 0.02]
##      [0.02, 0.03]
## OK: Residuals appear to be independent and not autocorrelated (p = 0.642).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.750).
## OK: Residuals appear to be independent and not autocorrelated (p = 0.606).

Cubic model

## 
## Call:
## lm(formula = rdt_cub_fw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.69603 -0.23190 -0.00395  0.20977  0.86734 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -3.786e-01  3.398e-01  -1.114  0.26712    
## container            1.663e-01  2.055e-01   0.809  0.41985    
## time                -1.801e-02  1.498e-02  -1.202  0.23140    
## I(time^2)           -4.194e-04  4.119e-04  -1.018  0.31032    
## I(time^3)           -2.782e-06  3.117e-06  -0.893  0.37362    
## tueE                 8.824e-02  6.115e-02   1.443  0.15121    
## wedE                -4.974e-02  6.044e-02  -0.823  0.41192    
## thuE                -8.627e-02  5.865e-02  -1.471  0.14356    
## friE                 2.585e-02  5.744e-02   0.450  0.65339    
## satE                -8.667e-02  6.045e-02  -1.434  0.15382    
## temp_c               7.168e-04  4.429e-03   0.162  0.87165    
## humi_p               2.358e-03  3.066e-03   0.769  0.44303    
## prcp_mm             -2.536e-02  1.350e-02  -1.879  0.06231 .  
## liquors              9.002e-03  1.732e-02   0.520  0.60404    
## sales                1.237e-03  1.873e-04   6.604 7.42e-10 ***
## halfs                3.164e-02  9.541e-03   3.317  0.00116 ** 
## container:time       3.111e-02  2.290e-02   1.359  0.17642    
## container:I(time^2)  1.233e-04  7.005e-04   0.176  0.86048    
## container:I(time^3)  4.615e-06  5.646e-06   0.817  0.41508    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3216 on 142 degrees of freedom
## Multiple R-squared:  0.5679, Adjusted R-squared:  0.5132 
## F-statistic: 10.37 on 18 and 142 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = rdt_cub_sfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38966 -0.14393 -0.02821  0.12109  0.83724 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -2.812e-01  2.215e-01  -1.269   0.2064    
## container            1.143e-01  1.340e-01   0.853   0.3949    
## time                -1.654e-02  9.769e-03  -1.693   0.0927 .  
## I(time^2)           -3.585e-04  2.686e-04  -1.335   0.1841    
## I(time^3)           -2.139e-06  2.032e-06  -1.053   0.2943    
## tueE                 8.830e-02  3.987e-02   2.215   0.0284 *  
## wedE                -6.790e-03  3.941e-02  -0.172   0.8634    
## thuE                -6.675e-02  3.824e-02  -1.746   0.0831 .  
## friE                 1.894e-02  3.745e-02   0.506   0.6138    
## satE                -5.644e-02  3.941e-02  -1.432   0.1543    
## temp_c              -1.657e-04  2.888e-03  -0.057   0.9543    
## humi_p               5.796e-04  1.999e-03   0.290   0.7723    
## prcp_mm             -1.566e-02  8.801e-03  -1.780   0.0772 .  
## liquors              6.430e-03  1.129e-02   0.569   0.5700    
## sales                7.385e-04  1.221e-04   6.048 1.24e-08 ***
## halfs                9.366e-03  6.221e-03   1.506   0.1344    
## container:time       2.353e-02  1.493e-02   1.576   0.1174    
## container:I(time^2)  1.969e-04  4.567e-04   0.431   0.6670    
## container:I(time^3)  3.025e-06  3.682e-06   0.822   0.4127    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2097 on 142 degrees of freedom
## Multiple R-squared:  0.4578, Adjusted R-squared:  0.3891 
## F-statistic: 6.662 on 18 and 142 DF,  p-value: 7.678e-12
## 
## Call:
## lm(formula = rdt_cub_lfw_log, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63393 -0.19327 -0.00731  0.19770  0.71861 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -3.673e-01  3.058e-01  -1.201 0.231692    
## container            9.555e-02  1.850e-01   0.517 0.606278    
## time                -4.851e-03  1.348e-02  -0.360 0.719603    
## I(time^2)           -1.110e-04  3.707e-04  -0.300 0.764982    
## I(time^3)           -8.657e-07  2.806e-06  -0.309 0.758107    
## tueE                 2.825e-02  5.504e-02   0.513 0.608519    
## wedE                -5.439e-02  5.440e-02  -1.000 0.319056    
## thuE                -7.139e-02  5.279e-02  -1.352 0.178412    
## friE                 3.461e-02  5.170e-02   0.670 0.504253    
## satE                -6.142e-02  5.441e-02  -1.129 0.260853    
## temp_c               2.051e-04  3.986e-03   0.051 0.959033    
## humi_p               2.427e-03  2.759e-03   0.879 0.380651    
## prcp_mm             -1.826e-02  1.215e-02  -1.503 0.135063    
## liquors              6.175e-03  1.559e-02   0.396 0.692635    
## sales                1.021e-03  1.686e-04   6.057 1.18e-08 ***
## halfs                3.124e-02  8.588e-03   3.638 0.000384 ***
## container:time       1.567e-02  2.061e-02   0.760 0.448497    
## container:I(time^2) -1.190e-04  6.305e-04  -0.189 0.850623    
## container:I(time^3)  2.231e-06  5.082e-06   0.439 0.661277    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2894 on 142 degrees of freedom
## Multiple R-squared:  0.5655, Adjusted R-squared:  0.5104 
## F-statistic: 10.27 on 18 and 142 DF,  p-value: < 2.2e-16

logged Scatter plot

logged Food waste plots

log-linear Local Regression

No interaction log RDiT - within month

## 
## Call:
## lm(formula = log_food_waste_kg ~ container, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.94497 -0.28651  0.05364  0.33439  0.93193 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.94497    0.09182  10.292 7.68e-14 ***
## container    0.08319    0.12860   0.647    0.521    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4591 on 49 degrees of freedom
## Multiple R-squared:  0.008468,   Adjusted R-squared:  -0.01177 
## F-statistic: 0.4185 on 1 and 49 DF,  p-value: 0.5207
## 
## Call:
## lm(formula = log_solid_waste_kg ~ container, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.44841 -0.14830 -0.07685  0.16641  0.64767 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.448409   0.048507   9.244 2.56e-12 ***
## container   0.002533   0.067936   0.037     0.97    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2425 on 49 degrees of freedom
## Multiple R-squared:  2.836e-05,  Adjusted R-squared:  -0.02038 
## F-statistic: 0.00139 on 1 and 49 DF,  p-value: 0.9704
## 
## Call:
## lm(formula = log_liquid_waste_kg ~ container, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.77353 -0.30531  0.09397  0.30715  0.80692 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.72440    0.08085   8.959 6.78e-12 ***
## container    0.09791    0.11324   0.865    0.391    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4043 on 49 degrees of freedom
## Multiple R-squared:  0.01503,    Adjusted R-squared:  -0.005074 
## F-statistic: 0.7476 on 1 and 49 DF,  p-value: 0.3915

Interaction - With in Month

## 
## Call:
## lm(formula = log_food_waste_kg ~ container * time, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.98510 -0.28823  0.06287  0.34733  0.92676 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.8975439  0.1929489   4.652  2.7e-05 ***
## container       0.1737246  0.2627721   0.661    0.512    
## time           -0.0036482  0.0129792  -0.281    0.780    
## container:time  0.0001996  0.0178381   0.011    0.991    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.468 on 47 degrees of freedom
## Multiple R-squared:  0.0118, Adjusted R-squared:  -0.05128 
## F-statistic: 0.1871 on 3 and 47 DF,  p-value: 0.9047
## 
## Call:
## lm(formula = log_solid_waste_kg ~ container * time, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.4677 -0.1351 -0.0628  0.1760  0.6442 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.4255827  0.1018912   4.177 0.000127 ***
## container       0.0546537  0.1387630   0.394 0.695463    
## time           -0.0017559  0.0068539  -0.256 0.798928    
## container:time -0.0005877  0.0094198  -0.062 0.950515    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2471 on 47 degrees of freedom
## Multiple R-squared:  0.004206,   Adjusted R-squared:  -0.05936 
## F-statistic: 0.06617 on 3 and 47 DF,  p-value: 0.9776
## 
## Call:
## lm(formula = log_liquid_waste_kg ~ container * time, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.79605 -0.28692  0.07517  0.30556  0.80295 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.6882743  0.1699780   4.049 0.000191 ***
## container       0.1671615  0.2314887   0.722 0.473801    
## time           -0.0027792  0.0114340  -0.243 0.809010    
## container:time  0.0001296  0.0157145   0.008 0.993453    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4123 on 47 degrees of freedom
## Multiple R-squared:  0.01753,    Adjusted R-squared:  -0.04519 
## F-statistic: 0.2795 on 3 and 47 DF,  p-value: 0.8399

Interaction - b/w week and month

log-linear Multiple - month

## 
## Call:
## lm(formula = log_food_waste_kg ~ container * time + temp_c + 
##     humi_p + prcp_mm + tueE + wedE + thuE + friE + satE + liquors + 
##     sales + halfs, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.51357 -0.16849  0.01946  0.12329  0.61325 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     0.2988962  0.6895540   0.433  0.66726   
## container       0.0751821  0.1844288   0.408  0.68595   
## time           -0.0035192  0.0090010  -0.391  0.69812   
## temp_c          0.0069893  0.0076565   0.913  0.36739   
## humi_p         -0.0036874  0.0071753  -0.514  0.61047   
## prcp_mm        -0.0482459  0.0274499  -1.758  0.08732 . 
## tueE            0.1637430  0.1050361   1.559  0.12776   
## wedE            0.0131842  0.1098702   0.120  0.90515   
## thuE           -0.0631627  0.0994321  -0.635  0.52929   
## friE            0.0006048  0.0987478   0.006  0.99515   
## satE           -0.1848926  0.1050318  -1.760  0.08684 . 
## liquors         0.0040398  0.0296279   0.136  0.89230   
## sales           0.0012807  0.0003682   3.478  0.00134 **
## halfs           0.0303484  0.0196676   1.543  0.13156   
## container:time  0.0092436  0.0137591   0.672  0.50599   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3018 on 36 degrees of freedom
## Multiple R-squared:  0.6852, Adjusted R-squared:  0.5627 
## F-statistic: 5.596 on 14 and 36 DF,  p-value: 1.496e-05
## 
## Call:
## lm(formula = log_solid_waste_kg ~ container * time + temp_c + 
##     humi_p + prcp_mm + tueE + wedE + thuE + friE + satE + liquors + 
##     sales + halfs, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.23587 -0.09713 -0.00118  0.07621  0.37761 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.2503976  0.3792951   0.660 0.513350    
## container       0.0017171  0.1014466   0.017 0.986589    
## time           -0.0009035  0.0049511  -0.182 0.856225    
## temp_c          0.0076969  0.0042115   1.828 0.075913 .  
## humi_p         -0.0035071  0.0039469  -0.889 0.380123    
## prcp_mm        -0.0125956  0.0150991  -0.834 0.409673    
## tueE            0.0361610  0.0577760   0.626 0.535340    
## wedE            0.0311853  0.0604350   0.516 0.609000    
## thuE           -0.0499517  0.0546935  -0.913 0.367160    
## friE            0.0180888  0.0543171   0.333 0.741050    
## satE           -0.0788150  0.0577736  -1.364 0.180972    
## liquors         0.0058179  0.0162971   0.357 0.723185    
## sales           0.0007934  0.0002025   3.918 0.000383 ***
## halfs           0.0044730  0.0108184   0.413 0.681720    
## container:time  0.0012049  0.0075683   0.159 0.874395    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.166 on 36 degrees of freedom
## Multiple R-squared:  0.6558, Adjusted R-squared:  0.5219 
## F-statistic: 4.899 on 14 and 36 DF,  p-value: 5.863e-05
## 
## Call:
## lm(formula = log_liquid_waste_kg ~ container * time + temp_c + 
##     humi_p + prcp_mm + tueE + wedE + thuE + friE + satE + liquors + 
##     sales + halfs, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52081 -0.14938  0.01322  0.14151  0.59771 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    -0.0146367  0.6279620  -0.023  0.98153   
## container       0.0843277  0.1679554   0.502  0.61867   
## time           -0.0031940  0.0081970  -0.390  0.69909   
## temp_c          0.0024800  0.0069726   0.356  0.72416   
## humi_p         -0.0006411  0.0065344  -0.098  0.92239   
## prcp_mm        -0.0486593  0.0249981  -1.947  0.05943 . 
## tueE            0.1400310  0.0956541   1.464  0.15189   
## wedE           -0.0282689  0.1000564  -0.283  0.77916   
## thuE           -0.0598792  0.0905507  -0.661  0.51264   
## friE            0.0087874  0.0899275   0.098  0.92270   
## satE           -0.1478034  0.0956502  -1.545  0.13103   
## liquors         0.0050597  0.0269815   0.188  0.85230   
## sales           0.0009589  0.0003353   2.860  0.00701 **
## halfs           0.0333015  0.0179109   1.859  0.07118 . 
## container:time  0.0099003  0.0125301   0.790  0.43463   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2749 on 36 degrees of freedom
## Multiple R-squared:  0.6655, Adjusted R-squared:  0.5354 
## F-statistic: 5.116 on 14 and 36 DF,  p-value: 3.793e-05

log-linear Multi - b/w week and month

Quadratic - b/w week and month

Cubic - b/w week and month

Local Regression per Customer

No interaction per Customer RDiT - within month

## 
## Call:
## lm(formula = food_waste_p_kg ~ container, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.071951 -0.021391  0.001999  0.021733  0.079921 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.066985   0.007257   9.230 2.69e-12 ***
## container   0.016731   0.010164   1.646    0.106    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03629 on 49 degrees of freedom
## Multiple R-squared:  0.0524, Adjusted R-squared:  0.03306 
## F-statistic: 2.709 on 1 and 49 DF,  p-value: 0.1062
## 
## Call:
## lm(formula = solid_waste_p_kg ~ container, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.022725 -0.006960 -0.002115  0.007308  0.025352 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.022725   0.002242  10.135 1.29e-13 ***
## container   0.001804   0.003140   0.575    0.568    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01121 on 49 degrees of freedom
## Multiple R-squared:  0.006691,   Adjusted R-squared:  -0.01358 
## F-statistic: 0.3301 on 1 and 49 DF,  p-value: 0.5682
## 
## Call:
## lm(formula = liquid_waste_p_kg ~ container, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.056246 -0.019655  0.000813  0.019476  0.068086 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.044261   0.005547   7.979 2.06e-10 ***
## container   0.014926   0.007769   1.921   0.0605 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02774 on 49 degrees of freedom
## Multiple R-squared:  0.07005,    Adjusted R-squared:  0.05107 
## F-statistic: 3.691 on 1 and 49 DF,  p-value: 0.06053

Interaction - With in Month

## 
## Call:
## lm(formula = food_waste_p_kg ~ container * time, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.076915 -0.019486 -0.000832  0.025310  0.076839 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.0552496  0.0151211   3.654 0.000649 ***
## container       0.0233299  0.0205930   1.133 0.263003    
## time           -0.0009027  0.0010172  -0.888 0.379327    
## container:time  0.0013136  0.0013979   0.940 0.352184    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.03667 on 47 degrees of freedom
## Multiple R-squared:  0.07158,    Adjusted R-squared:  0.01232 
## F-statistic: 1.208 on 3 and 47 DF,  p-value: 0.3172
## 
## Call:
## lm(formula = solid_waste_p_kg ~ container * time, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.025961 -0.006713 -0.002136  0.008028  0.024176 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.0189002  0.0046765   4.042 0.000195 ***
## container       0.0054568  0.0063688   0.857 0.395900    
## time           -0.0002942  0.0003146  -0.935 0.354488    
## container:time  0.0003079  0.0004323   0.712 0.479863    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01134 on 47 degrees of freedom
## Multiple R-squared:  0.02488,    Adjusted R-squared:  -0.03736 
## F-statistic: 0.3997 on 3 and 47 DF,  p-value: 0.7538
## 
## Call:
## lm(formula = liquid_waste_p_kg ~ container * time, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.059985 -0.016844  0.000476  0.019769  0.065107 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     0.0363494  0.0115661   3.143   0.0029 **
## container       0.0178730  0.0157515   1.135   0.2623   
## time           -0.0006086  0.0007780  -0.782   0.4380   
## container:time  0.0010057  0.0010693   0.941   0.3517   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02805 on 47 degrees of freedom
## Multiple R-squared:  0.08762,    Adjusted R-squared:  0.02938 
## F-statistic: 1.504 on 3 and 47 DF,  p-value: 0.2256

Interaction - b/w week and month

Multiple - month

## 
## Call:
## lm(formula = food_waste_p_kg ~ container * time + temp_c + humi_p + 
##     prcp_mm + tueE + wedE + thuE + friE + satE + liquors + sales + 
##     halfs, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.053369 -0.022131 -0.003374  0.021734  0.075991 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)
## (Intercept)     1.014e-01  8.249e-02   1.230    0.227
## container       7.872e-03  2.206e-02   0.357    0.723
## time           -6.602e-04  1.077e-03  -0.613    0.544
## temp_c          1.270e-03  9.159e-04   1.386    0.174
## humi_p         -6.900e-04  8.583e-04  -0.804    0.427
## prcp_mm        -5.080e-03  3.284e-03  -1.547    0.131
## tueE            2.077e-02  1.256e-02   1.653    0.107
## wedE            2.879e-03  1.314e-02   0.219    0.828
## thuE           -6.504e-03  1.189e-02  -0.547    0.588
## friE           -2.812e-04  1.181e-02  -0.024    0.981
## satE           -1.764e-02  1.256e-02  -1.404    0.169
## liquors        -9.237e-05  3.544e-03  -0.026    0.979
## sales           4.438e-05  4.404e-05   1.008    0.320
## halfs           8.675e-04  2.353e-03   0.369    0.715
## container:time  1.612e-03  1.646e-03   0.979    0.334
## 
## Residual standard error: 0.0361 on 36 degrees of freedom
## Multiple R-squared:  0.3108, Adjusted R-squared:  0.04284 
## F-statistic:  1.16 on 14 and 36 DF,  p-value: 0.3451
## 
## Call:
## lm(formula = solid_waste_p_kg ~ container * time + temp_c + humi_p + 
##     prcp_mm + tueE + wedE + thuE + friE + satE + liquors + sales + 
##     halfs, data = .)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0153218 -0.0060254 -0.0003569  0.0044083  0.0251027 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     3.841e-02  2.444e-02   1.572   0.1248  
## container       6.886e-04  6.537e-03   0.105   0.9167  
## time           -1.981e-04  3.190e-04  -0.621   0.5386  
## temp_c          5.914e-04  2.714e-04   2.179   0.0359 *
## humi_p         -3.221e-04  2.543e-04  -1.266   0.2135  
## prcp_mm        -1.030e-03  9.730e-04  -1.059   0.2967  
## tueE            4.124e-03  3.723e-03   1.108   0.2754  
## wedE            5.441e-03  3.895e-03   1.397   0.1709  
## thuE           -3.284e-03  3.525e-03  -0.932   0.3576  
## friE            3.169e-04  3.500e-03   0.091   0.9284  
## satE           -4.874e-03  3.723e-03  -1.309   0.1988  
## liquors        -3.214e-04  1.050e-03  -0.306   0.7613  
## sales           2.659e-05  1.305e-05   2.037   0.0490 *
## halfs          -2.991e-04  6.972e-04  -0.429   0.6705  
## container:time  2.937e-04  4.877e-04   0.602   0.5508  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0107 on 36 degrees of freedom
## Multiple R-squared:  0.3355, Adjusted R-squared:  0.07711 
## F-statistic: 1.298 on 14 and 36 DF,  p-value: 0.2559
## 
## Call:
## lm(formula = liquid_waste_p_kg ~ container * time + temp_c + 
##     humi_p + prcp_mm + tueE + wedE + thuE + friE + satE + liquors + 
##     sales + halfs, data = .)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.045207 -0.017250 -0.003794  0.018052  0.063976 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     6.301e-02  6.452e-02   0.977    0.335  
## container       7.183e-03  1.726e-02   0.416    0.680  
## time           -4.621e-04  8.421e-04  -0.549    0.587  
## temp_c          6.782e-04  7.164e-04   0.947    0.350  
## humi_p         -3.680e-04  6.713e-04  -0.548    0.587  
## prcp_mm        -4.050e-03  2.568e-03  -1.577    0.124  
## tueE            1.664e-02  9.827e-03   1.694    0.099 .
## wedE           -2.562e-03  1.028e-02  -0.249    0.805  
## thuE           -3.220e-03  9.303e-03  -0.346    0.731  
## friE           -5.981e-04  9.239e-03  -0.065    0.949  
## satE           -1.277e-02  9.827e-03  -1.300    0.202  
## liquors         2.291e-04  2.772e-03   0.083    0.935  
## sales           1.780e-05  3.445e-05   0.517    0.609  
## halfs           1.167e-03  1.840e-03   0.634    0.530  
## container:time  1.318e-03  1.287e-03   1.024    0.313  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02824 on 36 degrees of freedom
## Multiple R-squared:  0.2919, Adjusted R-squared:  0.01648 
## F-statistic:  1.06 on 14 and 36 DF,  p-value: 0.4226

Multi - b/w week and month

Quadratic - b/w week and month